P edic ing Adso p ion o Wa e /O ganic Mix u es
Using Molecula Simula ion
Miguel Jo ge and Nigel A. Sea on
School o Enginee ing and Elec onics, Uni e si y o Edinbu gh, Edinbu gh, EH9 3JL, U.K.
The use o Mon e Ca lo simula ion o p edic he adso p ion o mix u es o pola and
nonpola species on ac i®a ed ca bon was in®es iga ed using wa e and e hane on BPL
ca bon as a p o o ype sys em. The s uc u e o he adso ben was modeled by an a ay
o sli -shaped po es, cha ac e ized by a po e-size dis ibu ion. The chemical he e ogene-
i y o he ca bon was aken in o accoun by including oxygen-con aining si es on he
su ace o he po es. The po e-size dis ibu ion was ob ained om pu e-e hane adso p-
ion on he same ca bon sample, while he concen a ion and dis ibu ion o su ace
si es we e de e mined by analyzing pu e-wa e adso p ion. Model p edic ions ag ee well
wi h expe imen al mul icomponen da a.
In oduc ion
A subs an ial p opo ion o indus ial adso p ion p ocesses
Ž
in ol e ca bon adso ben s Bansal e al., 1988; Si ca e al.,
.Ž
1996 . In many impo an applica ions such as ai pu i ica-
.
ion and pe sonal p o ec ion , he e is a need o selec i ely
adso b o ganic species om gas s eams con aining a ce ain
amoun o wa e apo . I is well known ha he p esence o
wa e in he eeds eam can signi ican ly a ec he e iciency
o he sepa a ion p ocess. Reduced adso p ion capaci ies and
ea lie b eak h ough imes ha e been epo ed o adso p-
ion o a wide ange o o ganics on ac i a ed ca bon in he
Ž
p esence o wa e Gong and Keene , 1993; Scameho n, 1979;
.
Shin e al., 2002 . The de elopmen o a me hod o p edic
he adso p ion o mix u es o wa e and o ganic species on
ac i a ed ca bon is, he e o e, essen ial o he e icien de-
sign o such p ocesses. This in u n equi es a de ailed unde -
s anding o he undamen al aspec s ha a ec adso p ion o
bo h pola and nonpola componen s.
The mos common app oach o p edic ing mul icompo-
nen adso p ion is based on classical he modynamic me h-
Ž.
ods. O hese, he ideal adso bed solu ion heo y IAST
Ž.
Mye s and P ausni z, 1965 is he s anda d me hod used in
indus y. I is based on he concep o sp eading p essu e and
assumes ha he adso bed phase is an ideal solu ion in equi-
lib ium wi h he bulk gas phase. Fo sys ems such as mix u es
o wa e and hyd oca bons adso bed on ac i a ed ca bon, he
IAST is likely o pe o m badly, since his sys em is a om
ideal. O he he modynamic me hods ha e he e o e been
Co espondence conce ning his a icle should be add essed o N. A. Sea on.
Ž.
p oposed. To ou knowledge, Okazaki e al. 1978 we e he
i s o a emp a p edic ion o mul icomponen adso p ion in
his ype o sys em. In hei me hod, wa e is adso bed by
capilla y condensa ion, while he adso p ion o he o ganic
species is he esul o h ee con ibu ions: adso p ion on he
d y adso ba e su ace, dissolu ion in o he condensed phase,
and adso p ion on o he we su ace. They applied his
me hod o bina y adso p ion o wa e and se e al o ganic
Ž.
species ace one, me hanol, benzene, and oluene on ac i-
a ed ca bon. Al hough he p edic ions we e in easonable
ag eemen wi h expe imen al da a, he me hod has he signi -
ican disad an age o equi ing la ge amoun s o da a as in-
Ž
pu apa om he pu e-componen adso p ion iso he ms, i
also equi es liquid-phase iso he ms o he o ganic species
.
in wa e and apo ᎐liquid equilib ium da a . A la e me hod,
Ž.
based on po en ial heo y, is due o Doong and Yang 1987 .
Thei me hod uses he concep o maximum a ailable po e
olume, oge he wi h he Dubinin-Radushke ich equa ion
Žand la e , he Dubinin-As akho equa ion; Doong and Yang,
.
1988 wi h pa ame e s ob ained om he pu e-componen
iso he ms. A sys em wi h no la e al in e ac ions be ween ad-
so bed species is assumed, bu he maximum a ailable mic o-
po e olume o a gi en species is educed by he amoun
adso bed o all o he componen s. This me hod was seen o
pe o m well o he same sys ems s udied by Okazaki e al.
Ž.
1978 . A simila app oach was used by La anchy and S oeckli
Ž.
1999 o p edic bina y adso p ion o wa e and 2-chlo op o-
pane on ac i a ed ca bon. Thei me hod is essen ially a sim-
pli ied o m o he Doong-Yang me hod using he Dubinin-
Augus 2003 Vol. 49, No. 8AIChE Jou nal 2059
As akho equa ion. La anchy and S oeckli also applied IAST,
coupled wi h he Dubinin-As akho equa ion o ep esen he
pu e-componen da a, o adso p ion o wa e o ganic mix-
u es. They concluded ha IAST pe o ms easonably well
when he o ganic componen is soluble in wa e , while hei
implemen a ion o he Doong-Yang me hod is equi ed o
wa e -insoluble o ganics. Simila conclusions we e d awn
Ž.
mo e ecen ly by Linde s e al. 2001 . Finally, he e o s o
Ž.
Appel e al. 1998 o desc ibe mul icomponen adso p ion by
using mix u e i ial coe icien s a e no ewo hy. These au-
ho s success ully applied his heo y o bina y wa e hexane
adso p ion on ac i a ed ca bon, by using he equa ion o Talu
Ž.
and Meunie 1996 o he pu e-componen wa e iso he ms.
Howe e , he calcula ion o he i ial mix u e coe icien s e-
qui es he i ing o mul icomponen da a, and, hence, hei
me hod was only applied in a co ela i e manne .
The he modynamic me hods desc ibed p e iously ha e
some impo an disad an ages: hey become inaccu a e as he
Ž
sys ems mo e away om ideali y in he sense o Raoul ’s
.
law , due o chemical dissimila i y among he adso p i e
species; hey equi e a signi ican amoun o expe imen al
da a; and hey gi e us no in o ma ion on he s uc u e o he
adso ben . Recen ly, an al e na i e app oach, based on s a is-
ical mechanical me hods such as densi y unc ional heo y
and molecula simula ion, has begun o be applied o mul i-
Ž
componen adso p ion p edic ion see Razmus and Hall,
1991; Sega a and Gland , 1994; Guse and O’B ien, 1998;
Pan e al., 1999; Vuong and Monson, 1999; Macedonia and
.
Maginn, 1999; and e e ences he ein . In pa icula , molecu-
la simula ion me hods ha e been shown o be ex emely
powe ul in p edic ing mul icomponen adso p ion in ac i-
a ed ca bon as well as in cha ac e izing he adso ben i sel
Ž.
Da ies and Sea on, 2000 . Molecula simula ion can be used
o ob ain in o ma ion abou he chemical and physical cha -
ac e is ics o he adso ben ha a ec he adso p ion o he
molecula species o in e es , using a limi ed amoun o ex-
pe imen al da a as inpu . Wi h his in o ma ion, a model ad-
so ben , ep esen a i e o he eal adso ben , can be con-
s uc ed and used o p edic adso p ion in he eal adso ben .
The e ec o physical and chemical changes on adso p ion
can also be in es iga ed using he model adso ben , he eby
using molecula simula ion as an adso ben design ool. In
his a icle, we a emp o de elop such a model o he case
o wa e o ganic mix u es.
Models o Ac i a ed Ca bon
Ac i a ed ca bons a e composed o g aphi e pla es s acked
Ž.
oge he in a mo e o less i egula way McEnaney, 1988 .
The in e s ices o hese pla es o m a ne wo k o in e con-
nec ed po es, be ween which adso p ion occu s. These ca -
bons a e usually mic opo ous and ha e a e y s ong a ini y
owa d hyd oca bons. Howe e , in spi e o hei gene ally hy-
d ophobic na u e, mos ac i a ed ca bons used in indus ial
applica ions a e seen o s ongly adso b wa e . This e ec is
due o he p esence o pola g oups ha appea on he edges
o he g aphi ic pla es o on de ec si es, as a consequence o
he ac i a ion p ocess. The mos common ypes a e oxygen-
con aining g oups, such as ca boxyl, ca bonyl, and hyd oxyl
Ž.
Boehm, 1994 . These g oups o m nuclea ion si es o wa e ,
inc easing he hyd ophilic p ope ies o he ca bon. Thus, he
s uc u e o he ca bon has a s ong e ec on adso p ion o
all chemical species, while he chemically he e ogeneous si es
a ec mainly he adso p ion o pola species. In he case o
wa e o ganic mix u es, bo h ypes o he e ogenei y mus be
aken in o accoun when de eloping a model o he adso -
ben .
The mos widely used model o he s uc u e o ac i a ed
ca bon is an a ay o sli -shaped po es, cha ac e ized by a
Ž.
po e-size dis ibu ion PSD . This model akes ad an age o
he shape o he g aphi e pla ele s and assumes ha he en-
i e ca bon can be ep esen ed by a bundle o in ini e po es
o sli shape, which a e in equilib ium wi h he bulk gas phase.
The o al adso p ion on he ca bon can hen be ela ed o he
Ž.Ž
PSD ia he adso p ion in eg al equa ion AIE Sea on e
.
al., 1989
⬁
NT,P,ys w
␳
T,P,y,wdw 1
Ž. Ž.
Ž. Ž .
H
ii
0
Ž.
whe e NT,P,yis he o al adso p ion o componen ia
i
empe a u e T, bulk-phase p essu e P, and composi ion y;
i
Ž.
␳
T,P,y,wis he mola densi y o he adso ben a he
i
Ž.Ž .
same condi ions in a po e o wid h w; w sdV dw is
mic
he PSD; and Vis he speci ic mic opo e olume o he
mic
adso ben . The single-po e iso he ms can be calcula ed in a
numbe o di e en ways, anging om mac oscopic models
like he Kel in equa ion o he mo e complex molecula sim-
ula ion me hods.
A emp s o include chemical he e ogenei y in model ca -
Ž.
bons ha e so a been ew. Sega a and Gland 1994 ha e
modeled ac i a ed ca bons as a diso de ed s acking o disk-
shaped g aphi ic pla ele s. Su ace pola i y was ep esen ed
by dipole momen s smea ed along he edges o he pla es.
Simula ed adso p ion iso he ms in his model we e compa ed
o expe imen al da a, bu he ag eemen was only quali a i e.
Ž.
Subsequen wo k Go don and Gland , 1997 sugges s ha
he smea ed dipoles a e oo homogeneous o ep esen he
pola i y o eal adso ben s, and ha a disc e e dis ibu ion o
pola i y would be mo e ealis ic. A la e model, by McCallum
Ž.
e al. 1999 , combined a disc e e ep esen a ion o he su -
ace si es wi h a PSD model o he ca bon s uc u e. The
PSD was de e mined by using densi y unc ional heo y o
analyze a ni ogen adso p ion iso he m, and su ace si es we e
andomly dis ibu ed on he su ace o he po es. Simpli ied
molecula models, based on squa e-well po en ials o mimic
hyd ogen bonding, we e employed o ep esen wa e
molecules and su ace oxygen a oms. The o al concen a ion
o pola si es on he ca bon was de e mined expe imen ally
by i a ion me hods and he in e ac ion po en ial be ween
wa e molecules and su ace si es was ob ained om a i o
low-p essu e wa e adso p ion da a. Ag eemen wi h expe i-
men was easonable. Howe e , he po en ial models igno e
he long- ange na u e o he elec os a ic in e ac ions among
wa e molecules, and be ween he wa e molecules and pola
su ace g oups. This makes i di icul o ex end he model o
Ž
mo e gene al cases such as o he empe a u es, mul icompo-
.
nen adso p ion . A mo e ecen model o ac i a ed ca bon
o include chemical he e ogenei y was p oposed by B ennan
Ž.
e al. 2001 . The s uc u e o he adso ben is ep esen ed by
a s acking o g aphi ic pla es o se e al sizes, which is op i-
Augus 2003 Vol. 49, No. 8 AIChE Jou nal2060
mized o ep oduce expe imen ally de e mined ca bon᎐
ca bon adial dis ibu ion unc ions by a p ocedu e e med
Ž
e e se Mon e Ca lo simula ion Thomson and Gubbins,
.
2000 . Chemical he e ogenei y was included by andomly
placing pola ca bonyl si es on he edges o he pla es. Al-
hough his model p o ides us wi h a mo e ealis ic ep esen-
a ion o ac i a ed ca bon, i is also ex emely complex, which
ca ies disad an ages such as e y compu a ionally demand-
ing simula ions and di icul y o applica ion o a wide ange
o adso ben s. To ou knowledge, no compa ison o his model
wi h an expe imen has ye been p esen ed.
The model p oposed he e is based on a PSD o ep esen
he physical s uc u e o he ac i a ed ca bon, combined wi h
pola su ace si es o desc ibe he chemical he e ogenei y.
This dis ibu ion is ob ained om he AIE using expe imen-
al da a o pu e-e hane adso p ion oge he wi h g and
Ž.
canonical Mon e Ca lo GCMC simula ion o calcula e he
single-po e iso he ms. We ha e included chemical he e o-
genei y in he model by placing pola oxygena ed si es on he
su ace o he po es, he concen a ion and dis ibu ion o
which a e ob ained om an analysis o expe imen al pu e-
wa e adso p ion. This model is expec ed o cap u e all he
undamen al cha ac e is ics o he adso ben ha a ec he
adso p ion o bo h pola and nonpola species, while e ain-
ing a deg ee o simplici y ha will enable i s use in an indus-
ial con ex .
Molecula Simula ion in Single Po es
We ha e used GCMC simula ion o calcula e equilib ium
adso p ion iso he ms in model po es. The Mon e Ca lo
me hod is a s ochas ic p ocess based on he laws o s a is ical
mechanics. In e ec , one samples a la ge numbe o molecu-
la con igu a ions ha a e consis en wi h a gi en se o
Ž.Ž.
mac oscopic he modynamic a iables Hill, 1960 . Fo mos
adso p ion calcula ions, he g and canonical ensemble is he
mos con enien . In his ensemble he empe a u e, olume,
and chemical po en ial a e kep cons an , while he o al
numbe o molecules is allowed o luc ua e. This si ua ion is
analogous o an adso p ion expe imen , and, hus, adso p ion
iso he ms can be ob ained om GCMC simula ions by calcu-
la ing he equilib ium adso bed densi y a each se o condi-
ions. In p ac ice, ins ead o ixing he chemical po en ial, i
is mo e con enien o speci y p ope ies o he bulk phase,
Ž. Ž.
such as p essu e Pand composi ion x. One mus hen
i
employ an app op ia e equa ion o s a e o calcula e he
chemical po en ial o he bulk phase. In he simula ions e-
po ed in his a icle, he Peng-Robinson equa ion o s a e
Ž.
Sandle , 1989 was used o his pu pose. The GCMC simu-
la ion me hod has been widely used and is well documen ed
ŽŽ.
see, o example, Allen and Tildesley 1989 and F enkel and
Ž..
Smi 1996 . De ails o he implemen a ion o his pa icu-
Ž
la sys em ha e been published elsewhe e Jo ge and Sea on,
.
2002a .
The simula ion cell is ec angula and is bounded in he
z-dimension by he po e walls, he dis ance be ween which
Ž.
de ines he po e wid h w. In bo h di ec ions pa allel o he
Ž.
walls xand y, pe iodic bounda y condi ions we e used o
ep esen a semi-in ini e po e. The leng h o he cell in hese
di ec ions was 3 nm, which is su icien o a oid any ini e-size
Ž.
e ec s Jo ge and Sea on, 2002b . E hane molecules we e
Table 1. Geome ic and Po en ial Pa ame e s
U
o he
Molecula Models Used in This Wo k
Pa ame e s G aphi e E hane Wa e Ca bonyl
Ž.
␴
nm 0.34 0.3512 0.3166 0.296
y1
Ž.
⑀
Jⴢmol 232.8 1162.3 650.2 879.6
Ž.
⌬nm 0.335 ᎏᎏᎏ
y3
Ž.
␳
nm 114 ᎏᎏᎏ
sŽ.
Bond leng h nm ᎏ0.2353 0.1 0.1233
Ž.
Bond angle ⬚ᎏᎏ109.47 ᎏ
yŽ.
qe ᎏᎏy0.8476 y0.5
qŽ.
qe ᎏᎏq0.4238 q0.5
U
Ž.
G aphi e pa ame e s we e aken om S eele 1974 ; e hane pa ame e s
Ž.
om C acknell and Nicholson 1994 ; wa e pa ame e s om Be endsen
Ž.
e al. 1987 ; ca bonyl pa ame e s om Jo gensen and Ti ado-Ri es
Ž.
1988 .
Ž.
ep esen ed by wo Lenna d-Jones L-J si es, one o each
CH g oup, wi h pa ame e s aken om he wo k o C ack-
3
Ž.
nell and Nicholson 1994 . The poin -cha ge SPC E model o
Ž.
Be endsen e al. 1987 was chosen o ep esen wa e
molecules. The in e ac ion be ween an L-J cen e in an ad-
so ba e molecule and each o he po e walls is gi en by he
Ž.
10-4-3 po en ial o S eele 1974 o g aphi e. The oxygena ed
si es on he su ace o he ca bon we e ep esen ed by ca -
bonyl g oups, desc ibed by he OPLS po en ial o C⫽O
Ž.
g oups in aminoacids Jo gensen and Ti ado-Ri es, 1988 .
This model is composed o an L-J cen e and a nega i e poin
cha ge o he oxygen a om and a posi i e poin cha ge on
he ca bon a om in he basal plane o g aphi e, as desc ibed
Ž.
in a p e ious publica ion Jo ge e al., 2002 . Geome ic and
po en ial pa ame e s o wa e , e hane, g aphi e, and ca -
bonyl si es a e gi en in Table 1. The po en ial be ween wo
poin cha ges is long- anged and i s calcula ion equi es he
use o special echniques. The ull ex en o hese long- ange
in e ac ions was accoun ed o using he me hod o Heyes
Ž.
and an Swol 1981 . C oss-species Lenna d-Jones pa ame-
e s we e calcula ed using he Lo en z-Be helo combining
ules.
When compa ing simula ion esul s wi h expe imen s, he
o me needs o be co ec ed o accoun o he di e ence
be ween absolu e and excess adso p ion. The esul o a sim-
ula ion is he o al adso p ion o each species in a model
po eᎏabsolu e adso p ion. On he o he hand, adso p ion
expe imen s measu e he di e ence be ween absolu e ad-
so p ion and he amoun o adso ba e ha would be p esen
unde he same he modynamic condi ions i he e we e no
in e ac ions wi h he adso ben ᎏexcess adso p ion. The sim-
ula ed absolu e adso p ion iso he ms a e con e ed o excess
iso he ms using he me hod p oposed by Da ies and Sea on
Ž.
1999 .
Po e-Size Dis ibu ion
Ž.
The PSD is ob ained om he AIE Eq. 1 , using expe i-
men al da a o he adso p ion o a pu e componen , which
gi es he numbe o moles adso bed, as a unc ion o empe -
Ž.
a u e and p essu e, NT,P,ys1 . As men ioned p e iously,
i
he single-po e iso he ms we e calcula ed by GCMC simula-
Ž.
ions. Equa ion 1 is hen sol ed o he PSD, w. This is an
ill-posed p oblem, as in p inciple an in ini e numbe o PSDs
can sa is y he expe imen al da a. We ha e used he me hod
Augus 2003 Vol. 49, No. 8AIChE Jou nal 2061
Ž.
o Da ies e al. 1999 o sol e he AIE. A b ie ou line o
his me hod is gi en nex .
Fi s , he AIE is disc e ized, using a numbe o quad a u e
poin s ha is less han o equal o he numbe o expe imen-
al da a poin s. In o de o a oid excessi e spikiness o he
PSD, a egula iza ion ac o is inco po a ed in he minimiza-
ion p ocedu e. The op imal egula iza ion ac o is de e -
mined by analyzing he e o o he i , using bo h gene al-
ized c oss- alida ion and L-cu es. This p ocedu e elimina es
he need o es ic he PSD o a speci ic unc ional o m,
while s ill ensu ing ha a physically meaning ul esul is ob-
ained. When es ablishing he quad a u e in e als, one mus
ake in o accoun he concep o ‘‘window o eliabili y,’’ i s
Ž.
in oduced by Guse e al. 1997 . Essen ially, his es ablishes
lowe and uppe limi s o he po e sizes ha can be eliably
iden i ied in a PSD analysis. The lowe limi is he smalles
po e ha he adso ba e o in e es can en e , while he uppe
limi is he la ges po e o which he single-po e iso he ms
a e s ill linea ly independen . Fo la ge po es, he adso p ion
will occu i ually independen ly on each po e wall, and he
po es will hen become indis inguishable om each o he . In
his me hod, all he po es abo e he uppe limi o eliabili y
a e accoun ed o in a single quad a u e in e al. The limi s
o eliabili y depend on he adso ba e, on he empe a u e,
Ž.
and on he p essu e. Da ies and Sea on 2000 ha e ecen ly
shown ha he window o eliabili y is ex emely impo an
when p edic ing adso p ion, while he esolu ion o he PSD
plays only a mino pa .
Acco ding o he p eceding p ocedu e, he disc e ized AIE
becomes
m
NT,P,y w
␳
T,P,y,w
␦
w2
Ž. Ž.
Ž. Ž .
Ý
ininn
ns1
whe e mis he numbe o quad a u e in e als used in he
analysis, wi h m-1 in e als lying wi hin he window o elia-
bili y and one in e al accoun ing o he adso p ion in all he
po es abo e he uppe limi .
Figu e 1. Po e-size dis ibu ion o BPL ac i a ed ca bon
de e mined om he analysis o pu e-e hane
adso p ion a 273, 298, and 323 K.
Figu e 2. Fi o he pu e-e hane expe imen al da a o
()
Russell and LeVan 1997 using he PSD o
Figu e 1.
Diamonds a e o da a a 273 K, open squa es a e o 298
K, and iangles a e o 323 K.
Ž.
Russell and LeVan 1997 ha e epo ed da a o he ad-
so p ion o pu e wa e , pu e e hane, and a ious mix u es o
hese componen s a empe a u es o 273, 298 and 323 K. We
ha e used he p eceding me hod o calcula e a PSD o BPL
ca bon based on hei expe imen al da a o e hane a all
h ee empe a u es. I was decided o use h ee empe a-
u es, a he han a single empe a u e as in ea lie wo k
Ž.
Da ies and Sea on, 1999 , because i was in ended o p edic
adso p ion o wa e e hane mix u es o e his empe a u e
ange. A e he single-po e iso he ms o e hane we e ob-
ained om GCMC simula ions, he AIE was sol ed using a
Ž.
nonlinea minimiza ion ou ine MINOS, 1988 in e aced
h ough he GAMS ma hema ical p og amming package
Ž.
GAMS, 1998 . The window o eliabili y was de e mined o
lie be ween app oxima ely 0.6 and 2 nm, and he maximum
Ž
esolu ion possible co esponding o he numbe o expe i-
.
men al da a poin s was used. The dis ibu ion wi h he op i-
Ž
mal egula iza ion he gene alized c oss- alida ion me hod
and he L-cu e yielded e y simila egula iza ion pa ame-
.
e s, esul ing in essen ially indis inguishable PSDs is shown
in Figu e 1, and he i o he expe imen al da a in Figu e 2.
The calcula ed PSD i s he expe imen al da a well o e he
en i e p essu e ange.
Chemical He e ogenei y
The PSD model o he s uc u e o he ca bon has been
success ul in p edic ing pu e- and mul icomponen adso p-
Ž.
ion in ol ing nonpola Da ies and Sea on, 1999 and weakly
Ž.
pola Heuchel e al., 1999 species. Howe e , as we ha e
discussed, a desc ip ion o he chemical he e ogenei y o he
ca bon is equi ed when highly pola species, like wa e , a e
conce ned. He e we a emp o include his ex a dimension
in o ou model ca bon by placing oxygen-con aining si es on
he su ace o he sli po es.
The beha io o he eal ca bon is likely o be an a e age
o he con ibu ions o a wide a ie y o chemical g oups
Ž. Ž
Boehm, 1994 . Howe e , bo h expe imen al Ba on e al.,
Augus 2003 Vol. 49, No. 8 AIChE Jou nal2062
.Ž.
1994 and molecula simula ion Jo ge e al., 2002 esul s
sugges ha he amoun o wa e adso bed on ac i a ed ca -
bon depends p ima ily on he concen a ion o oxygen on he
su ace, ega dless o i s unc ionali y. The e o e, we ha e as-
sumed ha all he pola si es p esen in he ca bon can be
ep esen ed by ca bonyl g oups.
As o he loca ion o hese si es, i is known ha hey
p edomina e nea he edges o he g aphi e pla es. Since ou
model ep esen s he ca bon s uc u e by a collec ion o
Ž.
semi-in ini e po es wi h no edges , we ha e chosen o place
he pola si es on a squa e la ice supe imposed on he po e
walls. Fu he mo e, he si es we e egula ly dis ibu ed and
sepa a ed by a leas 0.75 nm. These simpli ica ions will ha e
an e ec on he s uc u e o he adso bed wa e in he model,
which will be di e en om ha in eal ca bons. Howe e ,
we ha e obse ed om p e ious molecula simula ion s udies
ha he dis ibu ion o pola si es on he su ace o he ca -
bon has a s ong impac a low p essu e, bu almos no e ec
Ž.
on he amoun adso bed a high p essu es Jo ge e al., 2002 .
Ž
An analysis o pu e-wa e adso p ion a low p essu e p e e -
.
ably in he Hen y’s law limi migh , in p inciple, p o ide us
wi h in o ma ion on he si e dis ibu ion. Un o una ely, such
low-p essu e expe imen al da a a e ha d o come by and we e
una ailable o he pa icula ca bon unde s udy. Howe e ,
since mos o he a ailable expe imen al da a we e ob ained
Ž.
a high pa ial p essu es o wa e see Figu e 5 , he assump-
ion o a egula si e dis ibu ion in a po e wi h no edges
should ha e a negligible e ec on he esul s. Fu he mo e,
he si ua ion o echnological in e es , and di icul y, is when
wa e adso p ion on he ca bon is subs an ial, which means
ha o mos p ac ical cases, he p ecise dis ibu ion o he
pola si es on he ca bon su ace will no be an impo an
ac o .
The las ac o one mus conside is he dis ibu ion o po-
la si es be ween po es o di e en wid h. An ob ious i s
Ž
choice is simply o say ha his dis ibu ion is uni o m ha
.
is, all po es con ain he same densi y o ca bonyl g oups .
This assump ion, oge he wi h he p e ious ones, educes he
p ocess o cha ac e izing he chemis y o he ac i a ed ca -
bon o he de e mina ion o a single a iableᎏ he concen a-
Figu e 3. Po e-size dis ibu ion o BPL ac i a ed ca bon
educed o 15 disc e e po e sizes.
ion o ca bonyl g oups on he su ace. To es ima e his con-
cen a ion, we ha e i s loca ed he in lec ion poin in he
Ž.
expe imen al ypically S-shaped pu e-wa e adso p ion
Ž.
iso he m a 298 K see Figu e 5 . Then we ha e de e mined
he modal po e wid h o he PSD ob ained om pu e-e hane
Ž.
adso p ion Figu e 1 , which was calcula ed as 1.24 nm. A
se ies o GCMC simula ions in a model po e o ha wid h,
o di e en concen a ions o pola si es, was pe o med,
aking no e o he a ia ion o he p essu e o spon aneous
condensa ion wi h he si e concen a ion. The chosen con-
cen a ion was such ha he p essu e o spon aneous con-
densa ion in he single-po e iso he m co esponded oughly
o he in lexion poin o he expe imen al iso he m. This con-
cen a ion, 2.214
␮
mol m
2
, was used as a i s es ima e in
he model.
A e choosing he concen a ion o ca bonyl g oups, we
a e able o calcula e he o al pu e-wa e adso p ion iso he m
co esponding o he model ca bon. This in ol es calcula ing
a se ies o single-po e iso he ms by GCMC, one o each po e
size o he PSD, wi h he chosen concen a ion o pola si es.
Howe e , he e o in ol ed in calcula ing 57 di e en wa e
iso he ms is p ohibi i e, e en a e ully op imizing he calcu-
la ion o he long- anged po en ial o cha ged molecules. We
ha e he e o e educed he esolu ion o he o iginal PSD o
only 15 po es. This numbe was su icien o e ain all he
cha ac e is ics o he PSD, while signi ican ly educing he
compu a ion cos . The educed PSD is shown in Figu e 3 o
compa ison. I is wo h no ing ha he i o he pu e-e hane
adso p ion iso he ms using his educed PSD is essen ially
indis inguishable om ha ob ained wi h he o iginal PSD
Ž.
Figu e 2 . This is in ag eemen wi h he conclusions o Da ies
Ž.
and Sea on 2000 , co obo a ing hei s a emen ha he
esolu ion o he PSD is o mino impo ance when adso p-
ion p edic ion is conce ned. Some o he single-po e
iso he ms calcula ed om GCMC simula ion a e shown in
Figu e 4.
Figu e 4. GCMC adso p ion iso he ms o pu e wa e a
298 K in sli -shaped po es wi h a concen a-
ion o su ace si es o 2.214
␮
mol
m
2
and
di e en wid hs.
Filled squa es
ᎏ0.76 nm; open ci clesᎏ0.84 nm;
c osses
ᎏ0.89 nm; open ianglesᎏ1.04 nm; illed
ci cles
ᎏ1.24 nm; open squa esᎏ1.44 nm; illed iangles ᎏ
2.04 nm. The p essu e is educed by he sa u a ion p essu e
Ž.
a hesame empe a u e 3167Pa.
Augus 2003 Vol. 49, No. 8AIChE Jou nal 2063

We can see ha a low p essu e he e is ha dly any wa e
adso bed in he po es. A a ce ain cha ac e is ic p essu e
Ž.
speci ic o each po e wid h , he e is a s eplike inc ease in
he amoun adso bed, un il he po es a e comple ely illed.
This discon inuous ansi ion is e idence o capilla y conden-
sa ion, and was obse ed in all he iso he ms a his empe a-
u e, down o he smalles po e wid h. I is wo h no ing ha
du ing a GCMC simula ion in a semi-in ini e po e a subc i i-
cal condi ions, he ue equilib ium apo ᎐liquid ansi ion is
ne e a ained in p ac ice. Ins ead, du ing adso p ion calcu-
la ions, he apo like phase emains me as able up o p es-
Ž
su es well abo e equilib ium liquid me as abili y also occu s
.Ž .
du ing deso p ion uns Jo ge e al., 2002 . Thus, he e ical
s ep in he single-po e iso he ms ep esen s a nonequilib ium
w
spon aneous condensa ion p ocess. The equilib ium ansi-
Ž
ion can, howe e , be simula ed using special me hods Jo ge
.x
and Sea on, 2002b . The apo me as abili y ha occu s in
po ous solids du ing eal adso p ion expe imen s is no s ic ly
compa able o he co esponding phenomenon in a simula-
ion, as he dynamics o he simula ed and eal p ocesses a e
Ž.
dis inc Sa kiso and Monson, 2000; Schoen e al., 1989 .
Ž.
Howe e , Sa kiso and Monson 2000 ha e obse ed ha in
a complex po e s uc u e, he hys e esis a ising om GCMC
simula ions seems o co espond well o he expe imen al
hys e esis. Fu he mo e, ecen s udies in well-cha ac e ized
po ous ma e ials in ol ing mos ly open unconnec ed po es
Ž.
Ra iko i ch e al., 2001 show good ag eemen be ween sim-
ula ion and expe imen and sugges ha he expe imen al ad-
so p ion b anch is close o he poin o spon aneous conden-
sa ion in GCMC simula ion han o he equilib ium ansi-
ion. In ligh o his, we will assume ha he spon aneous
condensa ion p essu e ob ained om GCMC is a good ap-
p oxima ion o he alue obse ed expe imen ally.
The o al adso p ion iso he m o he model ca bon was
ob ained by subs i u ing he single-po e iso he ms and he
PSD in o Eq. 1, and calcula ing he amoun adso bed, N.
This iso he m is compa ed o he expe imen al da a in Figu e
5. As we can see om his igu e, he simula ed iso he m
does no cap u e he S-shape o he expe imen al iso he m.
Ins ead, i shows wo dis inc ‘‘s eps,’’ e lec ing he bimodal
cha ac e o he PSD. Ano he impo an obse a ion is ha
he simula ion esul s lie almos en i ely a lowe p essu es
han he expe imen , which sugges s ha he concen a ion
o su ace si es is oo high. In a mo e encou aging no e, he
alue o simula ed adso p ion a he bulk sa u a ion p essu e
closely ma ches he expe imen al alue, which lends u he
c edibili y o he ep esen a ion o he s uc u e o he ca -
bon.
We ha e epea ed he p ocedu e desc ibed ea lie o a
Ž
2
.
lowe concen a ion o ca bonyl si es 1.476
␮
mol m . The
simula ed iso he m is also shown in Figu e 5. The educ ion
in he su ace si e concen a ion shi s he iso he m o highe
p essu es, bu does no al e i s shape. In ac , he simula ion
esul s will e ain he bimodal cha ac e o any si e concen-
a ion. Changing he ype o oxygen-con aining g oup used
in he model, o changing he in e ac ion pa ame e s o he
ca bonyl g oup, would ha e a simila e ec on he simula ion
esul s. Choosing a di e en dis ibu ion o he si es on he
po e walls should b ing abou a signi ican change in he
low-p essu e egion o he single-po e iso he ms. Howe e ,
he wa e up ake is mainly a esul o capilla y condensa ion,
()
Figu e 5. Expe imen al da a o Russell and LeVan 1997
()
o pu e wa e a 298 K diamonds and
iso he ms om he model ca bon a wo di -
e en concen a ions o uni o mly dis ibu ed
2
()
ca bonyl si es: 2.214
␮
mol
m solid line and
2
()
1.476
␮
mol
m dashed line .
The do ed line connec ing he expe imen al da a poin s is a
guide o he eye.
which means ha he o al adso p ion iso he m would be i -
ually unchanged.
Since elaxing ou wo assump ions o uni o m si e ype
and egula si e dis ibu ion on he po e walls will no im-
p o e he compa ison be ween simula ion and expe imen , we
a e le wi h elaxing he hi d and las ᎏ he uni o m si e
dis ibu ion on po es o di e en wid h. We ha e now al-
lowed he densi y o ca bonyl si es in each o he 15 po es o
a y, while ying o ma ch he simula ion o he expe imen al
Ž
iso he m. This means using a si e densi y dis ibu ion a he
.
han a single o e all densi y alue o ep esen he chemical
he e ogenei y o he ca bon. Such a dis ibu ion was calcu-
la ed by i ing he simula ed iso he m o he expe imen al
Ž
pu e-wa e adso p ion da a. The op imal dis ibu ion which
.
we will e m dis ibu ion I is shown in Figu e 6, and he
co esponding i o he expe imen al pu e-wa e iso he m is
shown in Figu e 7.
Combining a PSD o he s uc u e o he ca bon wi h a
dis ibu ion o ca bonyl si es o desc ibe he chemical he e o-
Ž
genei y p o ided good i s o bo h pu e-e hane he i shown
in Figu e 2 is i ually una ec ed by he p esence o pola
.
si es and pu e-wa e adso p ion iso he ms. The dis ibu ion
o pola si es shows wo peaks, one a ound po es o 1.44 nm
in wid h and he o he a ound 0.76 nm. The la e peak is
somewha ill-de ined, due o he sho age o expe imen al
da a a low p essu e, and i is na u al o ask how a dis ibu-
ion ha omi ed his peak al oge he would pe o m. To ind
ou , we ha e calcula ed iso he ms o he model ca bon using
he wo dis ibu ions o su ace si es shown in Figu e 8. Dis-
ibu ion II is based on a no mal dis ibu ion cen e ed a ound
Ž
1.49 nm wi h a s anda d de ia ion o 0.3 nm he eby, inco -
po a ing he main peak o dis ibu ion I, bu neglec ing he
.
peak a low po e size , while dis ibu ion III is based on an
Ž
in e se exponen ial and is, he e o e, mono onically inc eas-
.
ing, unlike bo h dis ibu ions I and II . When calcula ing hese
Augus 2003 Vol. 49, No. 8 AIChE Jou nal2064
Figu e 6. Op imal dis ibu ion o pola si es on BPL ca -
bon de e mined by analysis o pu e-wa e ad-
()
so p ion a 298 K dis ibu ion I .
dis ibu ions, he densi y o su ace si es was ounded o o
allow o an in ege numbe o ca bonyl g oups in he simula-
ion cell.
In Figu e 9 we compa e he expe imen al iso he m wi h
he simula ed one, ob ained using dis ibu ions II and III. As
we can see, dis ibu ion II i s he expe imen al da a e y sa -
is ac o ily abo e a ela i e p essu e o 0.4. This is expec ed,
since he peak o dis ibu ion II closely esembles he second
Ž.
peak o dis ibu ion I he bes - i dis ibu ion . This peak lies
in he egion o la ge mic opo es, which a e esponsible o
he wa e up ake a high ela i e p essu es. Howe e , he
low-p essu e adso p ion is se e ely unde es ima ed; his can
also be ela ed o he pola si e dis ibu ion. The low-p es-
su e up ake is mainly dic a ed by adso p ion in he small mi-
c opo es. In dis ibu ion II, hese po es a e almos de oid o
pola si es, and, hus, condensa ion occu s much la e . The
i o expe imen is much wo se o he case o dis ibu ion
Figu e 7. Fi o he pu e-wa e expe imen al da a o
()
Russell and LeVan 1997 a 298 K on BPL
ca bon using he PSD o Figu e 1 and he po-
la si e dis ibu ion o Figu e 6.
The diamonds ep esen he expe imen al da a and he solid
line is he simula ed iso he m.
()
Figu e 8. Two ‘‘smoo h’’pola -si e dis ibu ions: a dis-
()
ibu ion II; b dis ibu ion III.
III. In ac , i is almos as bad as o he uni o m si e dis ibu-
ions shown p e iously. The eason o his is ha , because i
is mono onically inc easing, dis ibu ion III is unable o com-
()
Figu e 9. Expe imen al da a o Russell and LeVan 1997
()
o pu e wa e a 298 K diamonds and
iso he ms om he model ca bon wi h wo di -
e en dis ibu ions o ca bonyl si es: dis ibu-
()( )
ion II solid line and III dashed line .
Augus 2003 Vol. 49, No. 8AIChE Jou nal 2065
pensa e o he bimodal PSD, wi h he simula ed iso he m
e aining he wo dis inc s eps. F om his analysis, we can
conclude ha while a sui ably chosen unimodal dis ibu ion
o su ace si es can desc ibe he da a abo e a ela i e p es-
su e o a ound 0.4, below his p essu e he peak a small po e
size shown in dis ibu ion I mus be aken in o accoun . A
p ecise desc ip ion o he si e densi y in hese small po es is
di icul in he p esen case, due o he educed amoun o
expe imen al da a ob ained a low ela i e p essu e. In sum-
ma y, he p edic ed adso p ion o wa e is qui e sensi i e o
he p ecise o m o he pola si e dis ibu ion as a unc ion o
po e size.
We a e now able o compa e he physical p ope ies o ou
Ž
model ca bon composed o he PSD o Figu e 3 and he
.
pola si e dis ibu ion o Figu e 6 wi h hose o eal BPL
ca bon, de e mined expe imen ally. We ha e calcula ed he
Ž.
mic opo e olume, he speci ic su ace a ea Sand he su -
Ž.
ace oxygen concen a ion C o he model ca bon. The
O
o al olume o mic opo es o he model ca bon is gi en by
m
Vs w
␦
w3
Ž. Ž.
Ý
mic
nn
ns1
In o de o compa e his olume o he expe imen ally de e -
mined alues on he same basis, he esul o Eq. 3 was modi-
ied o accoun o he olume o he po e ha is inaccessible
wŽ. x
o he adso ba e molecules see Jo ge 2003 , o de ails .
The speci ic su ace a ea o he model is simply gi en by
m2 w
␦
w
Ž.
nn
Ss4
Ž.
Ýw
n
ns1
Finally, using he pola si e dis ibu ion and aking in o ac-
coun ha each ca bonyl g oup con ains one oxygen a om,
he o al concen a ion o oxygen on he model ca bon can be
ob ained om
m2 w
␦
w
Ž.
nn
Cscw 5
Ž. Ž.
Ý
O
n
w
n
ns1
Ž.
whe e cw is he mola concen a ion o ca bonyl si es pe
uni su ace a ea in a po e o wid h w.
Table 2 shows a compa ison be ween he speci ic p ope -
ies o he model wi h hose o eal BPL ca bon. B adley and
Ž.
Rand 1995 ha e ob ained a consis en alue o he o al
mic opo e olume o BPL ca bon by applying he Dubinin-
Radushke i ch equa ion o iso he ms o se e al nonpola ad-
Table 2. Speci ic P ope ies o BPL Ca bon om Expe imen-
al Measu emen s s. Those o he Model Ca bon
Model Expe imen
U
3
Ž.
Vcm g 0.417 0.43
mic UU
2
Ž.
Sm g 925 1,088y1,120
†
Ž.
Cmmol g 1.16 1.14y1.40
O
U
Ž.
Taken om B adley and Rand 1995 .
UU
Ž. Ž.
Taken om Ba on e al. 1998 , MacDonald e al. 2000 , and Mac-
Ž.
Donald and E ans 2002 .
†
Ž. Ž.
Taken om Ba on e al. 1996, 1997 , MacDonald e al. 2000 , and
Ž.
MacDonald and E ans 2002 .
so ba es. Ba on and cowo ke s ha e pe o med ex ensi e ex-
pe imen al cha ac e iza ion s udies on BPL ca bon. They
ha e ob ained speci ic su ace a eas by applying he s anda d
Ž
BET me hod o N adso p ion Ba on e al., 1998; MacDon-
2
.
ald e al., 2000; MacDonald and E ans, 2002 . They ha e also
pe o med a se ies o empe a u e-p og ammed deso p ion
s udies o de e mine he oxygen concen a ion on he su ace
Ž
o BPL ca bon Ba on e al., 1996; Ba on e al., 1997; Mac-
.
Donald e al., 2000; MacDonald and E ans, 2002 . In Table
2, he ange o su ace a eas and oxygen concen a ions ob-
ained on di e en samples is gi en.
The mic opo e olume o he model ca bon shows good
ag eemen wi h he expe imen al de e mina ion, bu he spe-
ci ic su ace a ea is sligh ly below he BET su ace a ea.
Howe e , i is likely ha he BET me hod o e es ima es he
eal speci ic a ea o he ca bon, since i does no ake in o
accoun he enhancemen o he adso p ion ene gy in small
po es. As o he oxygen concen a ion o he model, i is
wi hin he ange o independen ly de e mined alues. This
compa ison should only be aken as a ough guide, since he
oxygen a oms included in he model e ec i ely accoun o
all he di e en si es o a eal ca bon ha in e ac wi h wa-
e , including o he he e oa oms and basic si es. Ne e he-
less, he good ag eemen ob ained sugges s ha he app oach
p esen ed he e is physically easonable. The e o e, i can be
concluded ha bo h he s uc u e and he chemis y o he
model ca bon a e consis en wi h expe imen al da a ob ained
on eal BPL ca bon.
P edic ion o Mul icomponen Adso p ion
We ha e assessed he p edic i e capabili ies o he model
by compa ing simula ion esul s wi h expe imen al measu e-
men s o a mix u e o wa e and e hane on he same sample
o BPL. The adso p ion iso he m o he model was ob ained
by pe o ming GCMC simula ions in he 15 sli -shaped po es
conside ed p e iously, wi h a concen a ion o ca bonyl si es
gi en by he dis ibu ion o Figu e 6. These iso he ms we e
hen weigh ed by he PSD o Figu e 3, acco ding o Eq. 2, o
yield he o al adso p ion iso he m.
Figu e 10 shows a compa ison be ween he mul icompo-
nen adso p ion iso he ms ob ained om expe imen and
om molecula simula ion. The ag eemen is easonable, e en
hough he e is a sligh unde es ima ion o wa e up ake a
Ž
high pa ial p essu es o e hane co esponding o low mole
.
ac ions o wa e in he bulk mix u e . This is balanced by an
o e es ima ion o he e hane up ake in his egion. Wa e up-
ake a e y low mole ac ions o wa e is mainly dic a ed by
adso p ion in po es o wid h below 0.84 nm, since e hane is
p e e en ially adso bed in he la ge po es. This is p ecisely
he ange o po e sizes in which he pola si e dis ibu ion is
poo ly de ined. As explained p e iously, his is because o he
es ic ed amoun o a ailable expe imen al pu e-wa e da a
a low ela i e p essu e. I is, he e o e, no su p ising ha
he mul icomponen adso p ion p edic ions in his ange,
whe e he pola si e densi y has a pa icula ly s ong e ec
on adso p ion, a e poo e . The di e en adso p ion beha io
in po es o di e en sizes is illus a ed in Figu e 11, which
shows snapsho s ob ained om wa e e hane simula ions in
wo po es o di e en wid h and a a high e hane pa ial
Augus 2003 Vol. 49, No. 8 AIChE Jou nal2066
Figu e 10. Expe imen al da a o Russell and LeVan
() ( )
1997 o bina y wa e solid diamonds and
()
e hane open diamonds adso p ion a 298 K
(
wi h iso he ms om he model ca bon solid
)
line using he PSD o Figu e 3 and he po-
la -si e dis ibu ion o Figu e 6.
p essu e. As we can see, he smalle po e is illed wi h wa e ,
while he la ge po e con ains mos ly e hane molecules.
Again, i would be in e es ing o see wha he beha io o
he model ca bon would be, wi h espec o wa e e hane
mix u e adso p ion, i a uni o m ca bonyl si e dis ibu ion was
Ž.
assumed ins ead o dis ibu ion I . We ha e calcula ed he
Figu e 11. Molecula simula ion o a mix u e o e hane
()
pa ial p essu e s73,416 Pa and wa e
()
pa ial p essu e s1584 Pa a 298 K ad-
so bed on ac i a ed ca bon po es o wid h:
() ()
a 0.8 nm; b 1.24 nm.
The magen a sphe es ep esen he L-J cen e s o e hane,
he anspa en g ay sphe es ep esen he L-J cen e s o
wa e , and he g een sphe es ep esen he ca bonyl si es.
The poin cha ges o he models a e ep esen ed by solid
sphe es, blue o a nega i e cha ge and ed o posi i e.
Figu e 12. Expe imen al da a o Russell and LeVan
() ( )
1997 o bina y wa e solid diamonds and
()
e hane open diamonds adso p ion a 298 K
wi h iso he ms om he model ca bon using
he PSD o Figu e 3 and wo di e en con-
cen a ions o uni o mly dis ibu ed ca bonyl
2
()
si es: 2.214
␮
mol
m solid lines and 1.476
2
()
␮
mol
m dashed lines .
mul icomponen adso p ion iso he ms a he same condi-
ions, using wo di e en alues o he uni o m su ace si e
densi y in he po es. The esul s a e compa ed wi h he ex-
pe imen in Figu e 12. As we can see, he p edic ions a e
now ex emely poo , wi h wa e adso p ion being subs an-
ially o e es ima ed and e hane adso p ion unde es ima ed.
This is due o he la ge si e densi y in he po es a ound 1 nm,
which leads o a high wa e up ake in he en i e p essu e
ange. The e ec he e is analogous o he o e es ima ion o
he pu e-wa e adso p ion a ela i e p essu es below 0.5, is-
ible in Figu e 5. F om his analysis, he impo ance o a com-
ple e and de ailed desc ip ion o he chemical he e ogenei y
o he ac i a ed ca bon is once again emphasized.
We ha e also assessed he pe o mance o wo classical
he modynamic me hods o his sys em, namely he IAST
Ž.
Mye s and P ausni z, 1965 and he Doong-Yang me hod
Ž.
1988 . The implemen a ion o hese me hods was as de-
sc ibed in he o iginal a icles, excep whe e indica ed below.
In he case o he IAST, he in eg a ion o he pu e-compo-
nen iso he ms was pe o med nume ically by Simpson’s ule.
When ex apola ion o he pu e-e hane iso he m o high
p essu e was equi ed, his was done using he To h equa ion
Ž.
To h, 1962 . The nonideali y o he bulk gas phase was aken
in o accoun by calcula ing ugaci ies using he Peng-Robin-
son equa ion o s a e. In he case o he Doong-Yang me hod,
he Dubinin-As akho equa ion was i ed o he pu e-com-
ponen iso he ms. Al hough he me hod allows o di e en
limi ing po e olumes o each o he componen s, we ha e
Ž
used he same alue o bo h wa e and e hane using di e -
.
en olumes yielded no imp o emen o he p edic ions . The
p edic ions using IAST and he Doong-Yang me hod a e
p esen ed in Figu e 13.
As we can see, bo h me hods ail o co ec ly p edic he
bina y wa e adso p ion iso he m, subs an ially o e es ima -
ing he up ake. The IAST subs an ially o e p edic s he ad-
Augus 2003 Vol. 49, No. 8AIChE Jou nal 2067